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Journal of Mathematical Biology

, Volume 41, Issue 5, pp 455–475 | Cite as

Fractional step methods applied to a chemotaxis model

  • Rebecca Tyson
  • L.G. Stern
  • Randall J. LeVeque

Abstract.

A fractional step numerical method is developed for the nonlinear partial differential equations arising in chemotaxis models, which include density-dependent diffusion terms for chemotaxis, as well as reaction and Fickian diffusion terms. We take the novel approach of viewing the chemotaxis term as an advection term which is possible in the context of fractional steps. This method is applied to pattern formation problems in bacterial growth and shown to give good results. High-resolution methods capable of capturing steep gradients (from CLAWPACK) are used for the advection step, while the A-stable and L-stable TR-BDF2 method is used for the diffusion step. A numerical instability that is seen with other diffusion methods is analyzed and eliminated.

Keywords

Pattern Formation Diffusion Method Diffusion Term Numerical Instability Steep Gradient 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Rebecca Tyson
    • 1
  • L.G. Stern
    • 2
  • Randall J. LeVeque
    • 3
  1. 1.Department of Applied Mathematics, Box 352420, University of Washington, Seattle, WA 98195-2420, USA. e-mail: rebecca@amath.washington.eduUS
  2. 2.Cray Inc., 411 First Avenue South, Suite 600, Seattle, WA 98104-2860, USA. e-mail: stern@cray.comUS
  3. 3.Departments of Mathematics and Applied Mathematics, University of Washington, Seattle, WA 98195, USA. e-mail: rjl@amath.washington.eduUS

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